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Consider the binary operations * : RxxRr...

Consider the binary operations `* : RxxRrarrR` and `o : RxxRrarrR` defined as `a*b = |a – b|` and `aob = a, forall a, b in R` Show that ∗ is commutative but not associative, o is associative but not commutative. Further, show that ∀ `a, b, c in R`, `a * (b o c) = (a * b) o (a * c)`. [If it is so, we say that the operation ∗ distributes over the operation o]. Does o distribute over ∗? Justify your answer.

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
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  2. Let S = {a,b,c} and T = {1,2,3}. Find F^-1 of the folowing functions F...

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  3. Consider the binary operations * : RxxRrarrR and o : RxxRrarrR define...

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  4. Given a non-empty set X, let * : P(X)xxP(X)rarrP(X), be defined as A *...

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  5. Define a binary operation * on the set {0,1,2,3,4,5} as a*b = {:{(a+...

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  6. Let A = {– 1, 0, 1, 2}, B = {– 4, – 2, 0, 2} and f, g : A rarr B, be f...

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  7. Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, ...

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  8. Let A = {1, 2, 3} Then number of equivalence relations containing (1,...

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  9. Let f : R to R be the signum function defined as f(x) = {{:(1, x gt 0...

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  10. Number of binary operations on theset (a,b) is

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  11. Show that if A= { 1,2,3} and R ={(1,1),(2,2),(3,3) (1,2),(2,1),(2,3),...

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  12. Let R be the quivalence relation in the set Z of integerx given by: R ...

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  13. If A = {1,2,3} and f,g are relations corresponding to the subset of A ...

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  14. On the set N of all natural numbers, a relation R is defined as follow...

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  15. Show that the function f : R rarr R defined by : f(x) = x/(x^2+1) AA ...

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  16. Let A = (0,1,2,3) and define a relation R on A as follows R = (0,0),(0...

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  17. Let A = (1,2,3,……….,9) and R be the relation in AxxA defined by (a,b) ...

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  18. If f = (5,2),(6,3), g = (2,5),(3,6), write fog.

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  19. Let f : R rarr R be defined by f(x) = x^2 +1 Find the pre-image of 17

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  20. Let f : R rarr R be defined by f(x) = x^2 +1 Find the pre-image of -3

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